Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	43×	body	1280	valid
4.0ms	151×	body	80	valid
3.0ms	30×	body	640	valid
1.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ x 1.0) (- x 1.0))
0.0b	(/ x (+ x 1.0))
3.0b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

11.0ms	(/ (+ x 1.0) (- x 1.0))
5.0ms	(/ x (+ x 1.0))
56.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series206.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (+ x 1.0) (- x 1.0))
38.0ms	(/ x (+ x 1.0))
129.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	392	760
1	1379	726
2	5002	716

prune399.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
0.0b	(pow (/ x (+ x 1.0)) 3)
0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
3.0b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

354×	`*-un-lft-identity`
216×	`times-frac`
190×	`add-sqr-sqrt`
104×	`unpow-prod-down` `cube-prod`
78×	`add-cube-cbrt`
66×	`distribute-lft-out`
61×	`distribute-lft-out--`
44×	`difference-of-squares`
24×	`swap-sqr`
22×	`add-exp-log` `add-cbrt-cube`
18×	`associate-r` `associate-l`
16×	`associate-/r/`
14×	`sqr-pow`
13×	`pow1`
8×	`div-inv`
6×	`cbrt-undiv` `pow-unpow` `flip3-+` `div-exp` `flip-+` `add-log-exp`
4×	`cube-div` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `unswap-sqr`
3×	`flip3--` `flip--`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3`
1×	`difference-cubes` `pow2` `frac-times` `sub-neg` `pow-plus` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub`

Counts

4 → 303

Calls

4 calls:

31.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
8.0ms	(pow (/ x (+ x 1.0)) 3)
12.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
197.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series457.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (/ x (+ x 1.0)) (/ x (+ x 1.0)))
59.0ms	(pow (/ x (+ x 1.0)) 3)
64.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
292.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify63.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1164	2932
1	5002	2690

prune555.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ x (+ x 1.0)) 3)
0.1b	(pow (/ (+ x 1.0) (- x 1.0)) 3)
3.0b	(log (exp (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))))
3.0b	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

rewrite867.0ms

Algorithm

rewrite-expression-head

Rules

464×	`*-un-lft-identity`
240×	`times-frac`
228×	`add-sqr-sqrt`
164×	`unpow-prod-down` `cube-prod`
114×	`distribute-lft-out--`
80×	`distribute-lft-out` `difference-of-squares`
78×	`log-pow`
77×	`exp-prod`
44×	`add-cube-cbrt`
26×	`sqr-pow`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
7×	`pow1`
6×	`pow-unpow` `add-log-exp`
5×	`log-prod`
4×	`cube-div` `pow-exp` `div-inv` `rem-cube-cbrt`
3×	`flip3--` `flip--`
2×	`difference-cubes` `cbrt-undiv` `cube-mult` `pow-to-exp` `sub-neg` `pow-pow` `flip3-+` `unpow3` `div-exp` `exp-sum` `flip-+`
1×	`log-div` `exp-diff` `diff-log` `rem-log-exp` `frac-sub`

Counts

4 → 307

Calls

4 calls:

8.0ms	(pow (/ x (+ x 1.0)) 3)
12.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
628.0ms	(log (exp (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))))
193.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

series749.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (/ x (+ x 1.0)) 3)
67.0ms	(pow (/ (+ x 1.0) (- x 1.0)) 3)
307.0ms	(log (exp (- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))))
312.0ms	(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))

simplify144.0ms

Algorithm

egg-herbie

Counts

319 → 319

Iterations

Useful iterations: 2 (113.0ms)

Iter	Nodes	Cost
0	938	2888
1	4170	2693
2	5002	2613

prune523.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ (cbrt (+ x 1.0)) (- x 1.0)) 3)
0.2b	(cbrt (+ x 1.0))
12.5b	(* (* (+ x 1.0) (+ x 1.0)) (pow (/ (cbrt (+ x 1.0)) (- x 1.0)) 3))
19.0b	(- (pow (/ x (+ x 1.0)) 3) (* (* (+ x 1.0) (+ x 1.0)) (pow (/ (cbrt (+ x 1.0)) (- x 1.0)) 3)))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

177×	`*-un-lft-identity`
146×	`add-sqr-sqrt`
144×	`times-frac`
88×	`associate-r`
86×	`cbrt-prod`
85×	`unpow-prod-down` `cube-prod`
79×	`add-cube-cbrt`
36×	`cube-div`
32×	`frac-times`
28×	`distribute-lft-out--` `difference-of-squares`
27×	`add-exp-log`
25×	`flip3-+` `flip-+`
24×	`associate-*l/`
21×	`distribute-lft-out`
17×	`frac-sub`
12×	`prod-exp`
11×	`add-cbrt-cube`
10×	`associate-*r/`
8×	`associate-/r/` `unswap-sqr`
6×	`pow-exp` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`pow-to-exp` `pow-unpow` `div-exp` `cbrt-unprod` `sqr-pow`
2×	`cube-mult` `cbrt-div` `unpow3` `rem-cube-cbrt`
1×	`cbrt-undiv` `sub-neg` `pow-pow` `pow1/3` `diff-log` `associate-l` `*-commutative`

Counts

4 → 277

Calls

4 calls:

17.0ms	(pow (/ (cbrt (+ x 1.0)) (- x 1.0)) 3)
2.0ms	(cbrt (+ x 1.0))
93.0ms	(* (* (+ x 1.0) (+ x 1.0)) (pow (/ (cbrt (+ x 1.0)) (- x 1.0)) 3))
123.0ms	(- (pow (/ x (+ x 1.0)) 3) (* (* (+ x 1.0) (+ x 1.0)) (pow (/ (cbrt (+ x 1.0)) (- x 1.0)) 3)))

series699.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(pow (/ (cbrt (+ x 1.0)) (- x 1.0)) 3)
93.0ms	(cbrt (+ x 1.0))
86.0ms	(* (* (+ x 1.0) (+ x 1.0)) (pow (/ (cbrt (+ x 1.0)) (- x 1.0)) 3))
314.0ms	(- (pow (/ x (+ x 1.0)) 3) (* (* (+ x 1.0) (+ x 1.0)) (pow (/ (cbrt (+ x 1.0)) (- x 1.0)) 3)))

simplify66.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1369	3601
1	5002	3226

prune630.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.1b

bsearch109.0ms

Steps

Iters	Range		Point
9	1610.1334651337936	588165898.4936482	11866.512480435778
9	-1898619.482837422	-0.12347723982223391	-10587.250289808897

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	40
1	48	40

end0.0ms

sample565.0ms

Algorithm

intervals

Results

186.0ms	1672×	body	1280	valid
112.0ms	1225×	body	640	valid
103.0ms	4139×	body	80	valid
46.0ms	659×	body	320	valid
14.0ms	305×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6